249 research outputs found
Spectral analysis of a massless charged scalar field with spacial cut-off
The quantum system of a massless charged scalar field with a self-interaction
is investigated. By introducing a spacial cut-off function, the Hamiltonian of
the system is realized as a linear operator on a boson Fock space. It is proven
that the Hamiltonian strongly commutes with the total charge operator. This
fact implies that the state space of the charged scalar field is decomposed
into the infinite direct sum of fixed total charge spaces. Moreover, under
certain conditions, the Hamiltonian is bounded below, self-adjoint and has a
ground ground state for an arbitrarily coupling constant. A relation between
the total charge of the ground state and a number operator bound is also
revealed
Quantum Diagonalization Method in the Tavis-Cummings Model
To obtain the explicit form of evolution operator in the Tavis-Cummings model
we must calculate the term explicitly which is very hard. In this paper we try to make the
quantum matrix diagonal to
calculate and, moreover, to know a deep structure of the model.
For the case of one, two and three atoms we give such a diagonalization which
is first nontrivial examples as far as we know, and reproduce the calculations
of given in quant-ph/0404034. We also give a hint to an
application to a noncommutative differential geometry.
However, a quantum diagonalization is not unique and is affected by some
ambiguity arising from the noncommutativity of operators in quantum physics.
Our method may open a new point of view in Mathematical Physics or Quantum
Physics.Comment: Latex files, 21 pages; minor changes. To appear in International
Journal of Geometric Methods in Modern Physic
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